1. A uniform electric field E = a i + b j intersects a surface of area A
A uniform electric field E = a i + b j intersects a surface of area A. Calculate the flux through this area if the surface lies:
in the XZ-plane.
in the YZ-plane.
in the XY-plane.
in the XZ-plane. [Answer: ΦXZ = (a i + b j).(A j) = bA.]
in the YZ-plane. [Answer: ΦYZ= (a i + b j).(A i) = aA.]
in the XY-plane. [Answer: ΦXY= (a i + b j).(A j) = 0.]

2. A) The electric field at e is zero.
Consider a spherical CONDUCTING shell with NO NET CHARGE, with a point charge, +Q, placed at its center. (For each statement select T True, F False).
A) The electric field at e is zero.
B) The electric field at a is zero.
C) The inner surface of the shell carries a charge −Q.
D) The electric field at c is zero
A) False, there is an enclosed charge, namely the point charge at the center. The overall shell has no net charge, however
B) False, it encloses the point charge.
C) True. Charge must reside on a surface. The interior of the shell cannot have any electric field. Thus, a Gaussian surface through c must have no field. The only way for there to be no field through c is for the Gaussian surface to enclose no net charge.
D) True,

3. C) True, shell acts like a point charge
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge −2q and the outer shell has a total charge +4 q
The radial component of the electric field in the region r< a is given by−2q/(4πε0r2).
The radial component of the electric field in the region c < r < d is given by−2q/(4πε0r2).
C) The radial component of the electric field in the region r>d is given by +2q/(4πε0r2).
A)False, the electric field is zero inside the shell.
B) False. There is no electric field inside of the shell.
C) True, shell acts like a point charge